On Social Networks that Support Learning

ABSTRACTBayes-rational agents reside on a social network. They take binary actions sequentially and irrevocably, and the right action depends on an unobservable state. Each agent receives a bounded private signal about the realized state and observes the actions taken by the neighbors who acted before. How does the network topology affect the ability of agents to aggregate the information dispersed over the population by means of the private signals? Most of the literature addressing such questions assumes that the network's structure is dictated by the order in which agents take their actions. By contrast, we assume that the network preexists and the order in which agents take actions is random. Hence, the network's topology is decoupled from the order of actions in a particular decision problem. The random order leads to a novel localization phenomenon: for most of the orders, agents have a bounded radius of influence, i.e., the agent's action is unlikely to affect those who are far from him in the network. This phenomenon underlies a bunch of new effects. Global information cascades become unlikely, and networks that fail to aggregate information exhibit many local cascades. The ability of an agent to learn the right action is determined by the local structure of the network around him, and there is a local topological condition guaranteeing that the agent takes the right action no matter how well others do. Roughly speaking, the condition requires that the agent bridges a multitude of mutually exclusive social circles. Networks, where this condition is satisfied for all agents, are robust to disruptions and keep aggregating information even if a substantial fraction of the population is eliminated adversarially. The full paper can be accessed at \hrefhttps://arxiv.org/pdf/2011.05255.pdf https://arxiv.org/pdf/2011.05255.pdf.